The numerical study of the system of hydrodynamic equations that include the director motion, fluid flow, and the temperature field redistribution across the hybrid-oriented liquid crystal (LC) cell under influence of the temperature gradient has been investigated. Calculations show that the horizontal LC layer being initially in the rest, if heated both from below or above, due to the temperature gradient, starts moving in the horizontal direction. It has been shown that the magnitude and direction of the hydrodynamic flow, excited by the temperature gradient, influence both the direction of the heat flow and the character of the preferred anchoring of the average molecular direction to the restricted surfaces. The role of the hydrodynamic flow in the relaxation processes, for a number of dynamic regime in 4-n-pentyl-4(')-cyanobiphenyl hybrid-oriented LC cell, also has been investigated.

The temperature-induced reorientation dynamics in microsized liquid crystal (LC) channel with a free LC/vacuum interface has been investigated theoretically based on the hydrodynamic theory including the director motion, the thermally excited fluid flow v, and the temperature T redistribution, produced by induced heating in the interior of the LC sample. Analysis of the numerical results shows that due to interaction between ∇T and the gradient of the director field ∇nˆ in the LC channel bounded by the free LC/vacuum interface, a thermally excited vortical fluid flow is maintained in the vicinity of the heat source. Calculations also show that in the case of the fast heating, the LC sample settles down to three-vortical flow regime, whereas in the case of the slow heating, the LC material settles down to bi-vortical flow regime. As for nematogenic material, we have considered the LC channel to be occupied by 4-n-pentyl-4′-cyanobiphenyl and investigated the effect of both ∇nˆ and ∇T on the magnitude and direction of v, as well as on the height of the LC film on the solid surface, for a number of heating and hydrodynamic regimes.

We have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across a two-dimensional (2D) hybrid-oriented liquid-crystal (HOLC) cell under the influence of a heat flow directed normal to the upper bounding surface, whereas on the rest boundaries the temperature is kept constant. Calculations based upon the nonlinear extension of the classical Ericksen-Leslie theory shows that the HOLC material under the influence of the heat flow, after some time, more than the time of relaxation, for instance, of the director field in the HOLC cell, settles down to the rest state regime, where the horizontal and vertical components of the velocity vector are equal to zero, and the temperature field across the LC cell finally reaches the value of temperature on the lower and two lateral bounding surfaces. The role of hydrodynamic flow in the relaxation processes of the temperature field to its equilibrium distribution across the 2D HOLC cell, containing 4-n-pentyl-4'-cyanobiphenyl, has been investigated, for a number of dynamic regimes.

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Dynamic field pumping principle has been developed utilizing the interactions of both the director and velocity fields and a temperature gradient inverted deltaT. The orientational dynamics in the hybrid-oriented liquid-crystal (HOLC) microvolume confined between two infinitely long coaxial cylinders under the influence of the radially directed inverted deltaT has been investigated. We have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across the HOLC cavity between two cylinders under the influence of inverted deltaT, when the liquid-crystal cavity is heated both from outer (inner) to inner (outer) bounding cylinders. Calculations show that under the influence of inverted deltaT the initially quiescent HOLC drop settles down to a stationary flow regime, with the horizontal u(st)(r) component of velocity. The effects of inverted deltaT , of the character of the preferred anchoring of the average molecular direction to the restricted cylinders, and of the size of the HOLC cavity on magnitude and direction of hydrodynamic flow--for a number of hydrodynamic regimes--has been investigated.